Minimum cost lexicographic evacuation flow finding in intuitionistic fuzzy networks

Abstract

Nowadays, various emergencies that are human-made or natural occur widely and threaten people’ lives and health. One of the most important evacuation tasks is the minimum cost lexicographic flow modelling task, which allows aggrieved to be transported to safe areas along the optimal transportation routes, taking into account the priority of shelters. It is inevitable that when modelling an evacuation scenario, an expert will encounter difficulties in setting network parameters due to the inherent uncertainty of a network, the rapid change in the nature of the movement, etc. Intuitionistic fuzzy sets allow simulating doubts and uncertainty of a decision-maker when choosing a membership function. Due to the increasing complexity of the decision-making problems, experts cannot assess all the network parameters correctly because much specific knowledge is required, and each expert cannot be familiar with all attributes equally. Therefore, different decision-makers should have different values for various attributes. The algorithm proposed incorporates the search for the order of reliable shelters according to the modified TOPSIS method and the minimum cost paths in intuitionistic fuzzy conditions based on the non-standard subtraction operation. A case study is conducted to verify the proposed algorithm.